A conveyor of the type referred to below first in the Summary of the Invention is, for example, described in the document DE 195 28 922 C2. In this known solution, the engagement finger provided on each pallet-carrying member is rigidly connected to the structure of said member. From U.S. Pat. No. 6,070,534 a pallet conveyor is known where the pallets are not recirculated and in which the pallets are forced to follow the conveyor chain along the conveyor upper run by one or two elastically biased fingers carried by each pallet supporting member.